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Gamma-Ray Burst in a Molecular Cloud: Destruction of Dust and H2, and Emergent SpectrumAug 14 2001A gamma ray burst with strong optical-UV emission occuring in a molecular cloud will photodissociate H2, photoionize H2, H, and He, and destroy dust grains. We model these processes, including time-dependent radiative transfer in both continuum radiation ... More

Global and Local Two-Sample Tests via RegressionDec 21 2018Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature, there have been ... More

Understanding the Low-Frequency Modes in Disordered Systems at Single-Particle LevelMar 15 2011Apr 01 2011Normal modes provide a fundamental basis for understanding crucial properties of solids, such as the thermal conductivity, the heat capacity and the sound propagation. While the normal modes are excellently described by plane waves in crystals, they are ... More

Disk-Evaporation Fed Corona: Structure and Evaporation Feature with Magnetic FieldJul 03 2007The disk-corona evaporation model naturally interprets many observational phenomena in black hole X-ray binaries, such as the truncation of an accretion disk and the spectral state transitions. On the other hand, magnetic field is known to play an important ... More

Full counting statistics of phonon-assisted Andreev tunneling through a quantum dot coupled to normal and superconducting leadsNov 10 2016Dec 27 2016We present a theoretical investigation for the full counting statistics of the Andreev tunneling through a quantum dot (QD) embedded between superconducting (SC) and normal leads in the presence of a strong on-site electron-phonon interaction using nonequilibrium ... More

Determining The Galactic Halo's Emission Measure from UV and X-ray ObservationsJun 08 2009We analyze a pair of Suzaku shadowing observations in order to determine the X-ray spectrum of the Galaxy's gaseous halo. We simultaneously fit the spectra with models having halo, local, and extragalactic components. The intrinsic intensities of the ... More

Antenna Current Optimization and Realizations for Far-Field Pattern ShapingNov 27 2017Aug 24 2018Far-field shaping of small antennas is a challenge and the realizations of non-dipole radiation of small to intermediate sized antennas are difficult. Here we examine the antenna bandwidth cost associated with such constraints, and in certain cases we ... More

Eliminating cracking during dryingMar 27 2013When colloidal suspensions dry, stresses build up and cracks often occur - a phenomenon undesirable for important industries such as paint and ceramics. We demonstrate an effective method which can completely eliminate cracking during drying: by adding ... More

Irreversible Samplers from Jump and Continuous Markov ProcessesAug 21 2016Mar 12 2018In this paper, we propose irreversible versions of the Metropolis Hastings (MH) and Metropolis adjusted Langevin algorithm (MALA) with a main focus on the latter. For the former, we show how one can simply switch between different proposal and acceptance ... More

Search for the Signatures of a New-Born Black Hole from the Collapse of a Supra-massive Millisecond Magnetar in Short GRB Light CurvesDec 12 2017`Internal plateau' followed by a sharp decay is commonly seen in short gamma-ray burst (GRB) light curves. The plateau component is usually interpreted as the dipole emission from a supra-massive magnetar, and the sharp decay may imply the collapse of ... More

Spin glass in semiconducting KFe$_{1.05}$Ag$_{0.88}$Te$_{2}$ single crystalsApr 20 2016We report discovery of KFe$_{1.05}$Ag$_{0.88}$Te$_{2}$ single crystals with semiconducting spin glass ground state. Composition and structure analysis suggest nearly stoichiometric I4/mmm space group but allow for the existence of vacancies, absent in ... More

Energy-Efficient Optimization for Physical Layer Security in Multi-Antenna Downlink Networks with QoS GuaranteeFeb 20 2013In this letter, we consider a multi-antenna downlink network where a secure user (SU) coexists with a passive eavesdropper. There are two design requirements for such a network. First, the information should be transferred in a secret and efficient manner. ... More

THEMIS Observations of the Magnetopause Electron Diffusion Region: Large Amplitude Waves and Heated ElectronsJan 16 2013We present the first observations of large amplitude waves in a well-defined electron diffusion region at the sub-solar magnetopause using data from one THEMIS satellite. These waves identified as whistler mode waves, electrostatic solitary waves, lower ... More

$K^*$ mesons with hidden charm arising from $KX(3872)$ and $KZ_c(3900)$ dynamicsMay 22 2018Aug 23 2018Inspired by the recent discovery of the pentaquark states $P_c(4450)$ and $P_c(4380)$, which can be viewed as excited nucleon states with hidden charm, we study the three-body interaction of a kaon and a pair of $D\bar{D}^*$ in isospin 0 and 1. We show ... More

Effects of excess Fe on upper critical field and magnetotransport in Fe1+y(Te1-xSx)zMar 10 2010We have investigated the upper critical field anisotropy and magnetotransport properties of Fe1.14(1)Te0.91(2)S0.09(2) single crystals in stable magnetic fields up to 35 T. The results show that u0Hc2(T) along the c axis and in the ab-plane exhibit saturation ... More

Pauli-limited upper critical field in Fe1+yTe1-xSexJan 11 2010Mar 10 2010In this work we investigated the temperature dependence of the upper critical field u0Hc2(T) of Fe1.02(3)Te0.61(4)Se0.39(4) and Fe1.05(3)Te0.89(2)Se0.11(2) single crystals by measuring the magnetotransport properties in stable dc magnetic fields up to ... More

On the two-body decay processes of the three-body $K^*(4307)$ resonanceApr 14 2019In a recent work, Phys. Lett. B785, 112 (2018), we reported the finding of a $K^*$ resonance with hidden charm content, arising from the $KD\bar D^*$ dynamics, where the $D\bar D^*$ system is treated as a $Z_c(3900)$ or $X(3872)$. With the motivation ... More

Is silicene stable in air? -- First principles study of oxygen adsorption and dissociation on siliceneOct 25 2013The oxygen adsorption and dissociation on pristine silicene surface are studied by use of first-principles in this letter. The oxygen adsorption and dissociation on pristine silicene surface are studied by use of first-principles in this letter. It is ... More

Phase Diagram of KxFe2-ySe2-zSz and the Suppression of its Superconducting State by an Fe2-Se/S Tetrahedron DistortionFeb 11 2011Sep 21 2011We report structurally tuned superconductivity in KxFe2-ySe2-zSz (0<=z<=2) phase diagram. Superconducting Tc is suppressed as S is incorporated into the lattice, eventually vanishing at 80% of S. The magnetic and conductivity properties can be related ... More

On methods to determine bounds on the Q-factor for a given directivityFeb 10 2017May 18 2017This paper revisit and extend the interesting case of bounds on the Q-factor for a given directivity for a small antenna of arbitrary shape. A higher directivity in a small antenna is closely connected with a narrow impedance bandwidth. The relation between ... More

Physical properties of KxNi2-ySe2 single crystalsNov 06 2012We have synthesized K0.95(1)Ni1.86(2)Se2 single crystals. The single crystals contain K and Ni deficiencies not observed in KNi2Se2 polycrystals. Unlike KNi2Se2 polycrystals, the superconductivity is absent in single crystals. The detailed physical property ... More

Structure and physical properties of new layered iron oxychalcogenide BaFe2OSe2Jun 25 2012We have successfully synthesized a new layered iron oxychalcogenide BaFe2OSe2 single crystal. This compound is built up of Ba and Fe-Se(O) layers alternatively stacked along the c-axis. The Fe-Se(O) layers contain double chains of edge-shared Fe-Se(O) ... More

Systematic study of proton-neutron pairing correlations in the nuclear shell modelJul 15 2011Oct 18 2011A shell-model study of proton-neutron pairing in $2p1f$ shell nuclei using a parametrized hamiltonian that includes deformation and spin-orbit effects as well as isoscalar and isovector pairing is reported. By working in a shell-model framework we are ... More

A model of the light curves of Gamma-Ray BurstsMar 10 2007Mar 27 2007An extreme Kerr black hole (BH) surrounded by a precessing disk is invoked to explain the light curves of gamma-ray bursts (GRBs) based on the coexistence of the Blandford-Znajek (BZ) and the magnetic coupling (MC) processes. The overall shape of the ... More

Extremal problems on saturation for the family of $k$-edge-connected graphsOct 20 2017Mar 03 2018Let $\mathcal{F}$ be a family of graphs. A graph $G$ is $\mathcal{F}$-saturated if $G$ contains no member of $\mathcal{F}$ as a subgraph but $G+e$ contains some member of $\mathcal{F}$ whenever $e\in E(\overline{G})$. The saturation number and extremal ... More

Load Balancing via Joint Transmission in Heterogeneous LTE: Modeling and ComputationFeb 26 2016As one of the Coordinated Multipoint (CoMP) techniques, Joint Transmission (JT) can improve the overall system performance. In this paper, from the load balancing perspective, we study how the maximum load can be reduced by optimizing JT pattern that ... More

Range Assignment for Power Optimization in Load-Coupled Heterogeneous NetworksFeb 26 2016We consider the problem of transmission energy op- timization via range assignment for Low Power Nodes (LPNs) in Long Term Evolution (LTE) Heterogenous Networks (HetNets). The optimization is subject to the load coupling model, where the cells interfere ... More

Optimizing Power and User Association for Energy Saving in Load-Coupled Cooperative LTEFeb 26 2016Jun 21 2017We consider an energy minimization problem for cooperative LTE networks. To reduce energy consumption, we investigate how to jointly optimize the transmit power and the association between cells and user equipments (UEs), by taking into consideration ... More

A Performance Study of Energy Minimization for Interleaved and Localized FDMAFeb 26 2016Jun 21 2017Optimal channel allocation is a key performance engineering aspect in single-carrier frequency-division multiple access (SC-FDMA). It is of significance to consider minimum sum power (Min-Power), subject to meeting specified user's demand, since mobile ... More

Range Assignment for Power Optimization in Load-Coupled Heterogeneous NetworksFeb 26 2016Jun 21 2017We consider the problem of transmission energy op- timization via range assignment for Low Power Nodes (LPNs) in Long Term Evolution (LTE) Heterogenous Networks (HetNets). The optimization is subject to the load coupling model, where the cells interfere ... More

Load Balancing via Joint Transmission in Heterogeneous LTE: Modeling and ComputationFeb 26 2016Jun 21 2017As one of the Coordinated Multipoint (CoMP) techniques, Joint Transmission (JT) can improve the overall system performance. In this paper, from the load balancing perspective, we study how the maximum load can be reduced by optimizing JT pattern that ... More

On the limit of spectral gap formation via Bragg's reflectionNov 29 2018Although it is well recognized that waves propagating in periodic media have forbidden gaps in the continuous spectrum, it is still yet unknown about the minimum number and depth of periodic modulations for clear spectral formation. This limit is explored ... More

A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: homogeneous relaxation and transport coefficientsOct 07 2018A fast spectral method (FSM) is developed to solve the Uehling-Uhlenbeck equation for quantum gas mixtures with generalized differential cross-sections. Spatially-homogeneous relaxation problems are used to demonstrate that the FSM conserves mass and ... More

Constraining Photon Mass by Energy-Dependent Gravitational Light BendingJun 06 2014In the standard model of particle physics, photons are mass-less particles with a particular dispersion relation. Tests of this claim at different scales are both interesting and important. Experiments in territory labs and several exterritorial tests ... More

On the non-realizability of braid groups by homeomorphismsAug 24 2018In this paper, we will show that the projection $\text{Homeo}^+(D^2_n)\to B_n$ does not have a section; i.e. the braid group $B_n$ cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary point-wise and $n$ marked points ... More

Section problems for configuration spaces of surfacesAug 26 2017Jul 30 2018In this paper we give a close-to-sharp answer to the basic questions: When is there a continuous way to add a point to a configuration of $n$ ordered points on a surface $S$ of finite type so that all the points are still distinct? When this is possible, ... More

Exotic arithmetic structure on the first Hurwitz tripletSep 09 2012May 21 2013We find that the first Hurwitz triplet possesses two distinct arithmetic structures. As Shimura curves $X_1$, $X_2$, $X_3$, whose levels are with norm 13. As non-congruence modular curves $Y_1$, $Y_2$, $Y_3$, whose levels are 7. Both of them are defined ... More

Vanishing estimates for fully bubbling solutions of $SU(n+1)$ Toda Systems at a singular sourceApr 20 2018For Gauss curvature equation (or more general Toda systems) defined on two dimensional spaces, the vanishing rate of certain curvature functions on blowup points is a key estimate for numerous applications. However, if these equations have singular sources, ... More

Scaling limit of random forests with prescribed degree sequencesApr 07 2017In this paper, we consider the random plane forest uniformly drawn from all possible plane forests with a given degree sequence. Under suitable conditions on the degree sequences, we consider the limit of a sequence of such forests with the number of ... More

Small trees in supercritical random forestsOct 07 2017We study the scaling limit of random forest with prescribed degree sequence in the regime that the largest tree consists of all but a vanishing fraction of nodes. We give a description of the limit of the forest consisting of the small trees, by relating ... More

$\ell$-adic GKZ hypergeometric sheaf and exponential sumsAug 07 2012Apr 26 2016To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the $\ell$-adic counterpart of the ... More

Liouville theorems and a Schwarz Lemma for holomorphic mappings between Kähler manifoldsJul 07 2018Aug 24 2018We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.-F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of $\mathbb{C}$ isometrically from ... More

Mean value theorems on manifoldsAug 24 2006We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as later results of Schoen-Yau, Michael-Simon, etc, on curved Riemannian manifolds. For the heat equation a mean value ... More

Nonlinear differential Galois theoryAug 20 2006Apr 23 2011Differential Galois theory has played important roles in the theory of integrability of linear differential equation. In this paper we will extend the theory to nonlinear case and study the integrability of the first order nonlinear differential equation. ... More

Equidistribution of expanding curves in homogeneous spaces and Diophantine approximation for square matricesNov 05 2013Nov 08 2015In this article, we study an analytic curve $\varphi: I=[a,b]\rightarrow \mathrm{M}(n\times n, \mathbb{R})$ in the space of $n$ by $n$ real matrices, and show that if $\varphi$ satisfies certain geometric conditions, then for almost every point on the ... More

$Sp_{2n}(F_{q^{2}})$-Invariants In Irreducible Unipotent Representations of $Sp_{4n}(F_{q})$Mar 28 2013We show that for any irreducible representation of $Sp_{4n}(F_{q})$, the subspace of all its $Sp_{2n}(F_{q^{2}})$-invariants is at most one-dimensional. In terms of Lusztig symbols, we give a complete list of irreducible unipotent representations of $Sp_{4n}(F_{q})$ ... More

Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular DataOct 28 2008We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello it ... More

Galois representations arising from twenty-seven lines on a cubic surface and the arithmetic associated with Hessian polyhedraDec 14 2006In the present paper, we will show that three apparently disjoint objects: Galois representations arising from twenty-seven lines on a cubic surface (number theory and arithmetic algebraic geometry), Picard modular forms (automorphic forms), rigid Calabi-Yau ... More

Bounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensionsOct 21 2015In this paper, we study the Tamagawa numbers of a crystalline representation over a tower of cyclotomic extensions under certain technical conditions on the representation. In particular, we show that we may improve the asymptotic bounds given in the ... More

Finite $W$-superalgebras for queer Lie superalgebrasDec 10 2010May 07 2012We initiate and develop the theory of finite $W$-superalgebras $\mathcal{W}_\chi$ associated to the queer Lie superalgebra $\g=\q(N)$ and a nilpotent linear functional $\chi \in \ev\g^*$. We show that the definition of the $W$-superalgebra is independent ... More

Factorisation of two-variable p-adic L-functionsApr 28 2013Let $f$ be a modular form which is non-ordinary at $p$. Kim and Loeffler have recently constructed two-variable $p$-adic $L$-functions associated to $f$. In the case where $a_p=0$, they showed that, as in the one-variable case, Pollack's plus and minus ... More

Preliminary computation of the gap eigenmode of shear Alfvén waves on LAPDNov 29 2018Characterizing the gap eigenmode of shear Alfv\'{e}n waves (SAW) and its interaction with energetic ions is important to the success of magnetically confined fusion. Previous studies have reported an experimental observation of the spectral gap of SAW ... More

Alfvénic gap eigenmode in a linear plasma with ending magnetic throatsNov 29 2018To guide the experimental design of a linear plasma device for studying the interaction between energetic ions and Alfv\'{e}nic gap eigenmode (AGE), this work computes AGE referring to fusion conditions in a ultra-long large plasma cylinder ended with ... More

Exact Algorithms With Worst-case Guarantee For Scheduling: From Theory to PracticeDec 06 2017This PhD thesis summarizes research works on the design of exact algorithms that provide a worst-case (time or space) guarantee for NP-hard scheduling problems. Both theoretical and practical aspects are considered with three main results reported. The ... More

New Conserved Quantities of the Incompressible Euler EquationsJul 30 2010Aug 03 2010We show two new conserved quantities for the three-dimensional incompressible Euler equations. Due to professor Lin's comments, these quantities are deeply related to the concept of topological degree and not new. I will post a new version soon.

Deformations and Rigidity of $\ell$-adic SheavesNov 12 2016May 10 2018Let $X$ be a smooth connected projective algebraic curve over an algebraically closed field, and let $S$ be a finite nonempty closed subset in $X$. We study deformations of $\overline{\mathbb F}_\ell$-sheaves. The universal deformation space is a formal ... More

A New History-Driven Algorithm to Calculate the Density of StatesNov 30 2011We present a new Monte Carlo algorithm applying a history-driven mechanism for the calculation of the density of states for classical statistical models. The new method is as efficient as the Wang-Landau method in sampling through the energy range. With ... More

Robust correlations between quadrupole moments of low-lying $2^+$ states within random-interaction ensemblesApr 10 2015Feb 26 2016In the random-interaction ensembles, three proportional correlations between quadrupole moments of the first two $I^{\pi}=2^+$ states robustly emerge, including $Q(2^+_1)=\pm Q(2^+_2)$ correlations consistently with realistic nuclear survey, and the $Q(2^+_2)=-\frac{3}{7}Q(2^+_1)$ ... More

A short note on doubly substochastic analog of Birkhoff's theoremJan 04 2018Let B be an n by n doubly substochastic matrix. We show that B can be written as a convex combination of no more than {\sigma}(B)+t subpermutation matrices, where {\sigma}(B) is the number of nonzero elements in B and t is the number of fully indecomposable ... More

The fundamental group, rational connectedness and the positivity of Kaehler manifoldsFeb 03 2019First a conjecture asserting that any compact K\"ahler manifold $N$ with $Ric^\perp>0$ must be simply-connected is confirmed by adapting the comass of $(p, 0)$-forms into a maximum principle via the viscosity consideration. Secondly the projectivity and ... More

Estimating class numbers over metabelian extensionsMar 30 2017Let $p$ be an odd prime and $L/K$ a $p$-adic Lie extension whose Galois group is of the form $\mathbb{Z}_p^{d-1}\rtimes \mathbb{Z}_p$. Under certain assumptions on the ramification of $p$ and the structure of an Iwasawa module associated to $L$, we study ... More

The Exterior Cubic L-function of GU(6) and Unitary Automorphic InductionMar 11 2019In this paper, we extend Ginzburg-Rallis' integral representation for the exterior cube automorphic $L$-function of ${\rm GL}_6\times {\rm GL}_1$ to that of the quasi-split unitary similitude group ${\rm GU}_6$ and establish its analytic properties to ... More

The cohomological support locus of pluricaonical sheaves and the Iitaka fibrationDec 16 2012Nov 28 2013Let $alb_X: X \rightarrow A$ be the Albanese map of a smooth projective variety and $f: X \rightarrow Y$ the fibration from the Stein factorization of $alb_X$. For a positive integer $m$, if $f$ and $m$ satisfy the assumptions AS(1,2), then the translates ... More

Product formulas on a unitary group in three variablesApr 27 2001Apr 30 2001We obtain some basic partial differential operators connected with nonholomorphic automorphic forms on $\Gamma \backslash U(2, 1)/K$. We give the corresponding Eisenstein series of weight $k$ and automorphic Green functions of weight $k$. Moreover, we ... More

Representations of Lie superalgebras in prime characteristic IIIOct 12 2009For a restricted Lie superalgebra g over an algebraically closed field of characteristic p > 2, we generalize the deformation method of Premet and Skryabin to obtain results on the p-power and 2-power divisibility of dimensions of g-modules. In particular, ... More

The number of fiberings of a surface bundle over a surfaceMar 20 2017For a closed manifold $M$, let Fib$(M)$ be the number of distinct fiberings of $M$ as a fiber bundle with fiber a closed surface. In this paper we give the first computation of Fib$(M)$ where $1<\text{Fib}(M)<\infty$ but $M$ is not a product. In particular, ... More

Hessian polyhedra, invariant theory and Appell hypergeometric partial differential equationsDec 03 2004Dec 16 2004It is well-known that Klein's lectures on the icosahedron and the solution of equations of fifth degree is one of the most important and influential books of 19th-century mathematics. In the present paper, we will give the complex counterpart of Klein's ... More

A new conception for computing gröbner basis and its applicationsDec 24 2010Dec 28 2010This paper presents a conception for computing gr\"{o}bner basis. We convert some of gr\"{o}bner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm. The new algorithm's finite termination problem can be described ... More

Hausdorff dimension of divergent diagonal geodesics on product of finite volume hyperbolic spacesMar 24 2013Nov 08 2015In this article, we consider the product space of several non-compact finite volume hyperbolic spaces, $V_1, V_2, \dots , V_k$ of dimension $n$. Let $\mathrm{T}^1(V_i)$ denote the unit tangent bundle of $V_i$ for each $i=1,\dots , k$, then for every $(v_1, ... More

Dictionary for Sparse Representation of Chirp Echo in Broadband RadarAug 01 2010Aug 03 2010A new dictionary for sparse representation of chirp echo in broadband radar is put forward in this paper. Different with chirplet decomposition which decomposes echo in time-frequency plane, the dictionary transforms the sparsity of target observed by ... More

On the Rate of Convergence of the Power-of-Two-Choices to its Mean-Field LimitMay 21 2016This paper studies the rate of convergence of the power-of-two-choices, a celebrated randomized load balancing algorithm for many-server queueing systems, to its mean field limit. The convergence to the mean-field limit has been proved in the literature, ... More

Global Well-posedness of Incompressible Elastodynamics in Two DimensionsFeb 26 2014Mar 23 2016We prove that for sufficiently small initial displacements in some weighted Sobolev space, the Cauchy problem of the systems of incompressible isotropic elastodynamics in two space dimensions admits a uniqueness global classical solution.

On Axially Symmetric Incompressible Magnetohydrodynamics in Three DimensionsDec 24 2012Nov 15 2013The global regularity for the incompressible magnetohydrodynamic equations (MHD) in three dimensions is a long standing open problem of fluid dynamics and PDE theory. The Navier-Stokes equations can be viewed as a special case of MHD with a constant magnetic ... More

Tackling Sequence to Sequence Mapping Problems with Neural NetworksOct 25 2018In Natural Language Processing (NLP), it is important to detect the relationship between two sequences or to generate a sequence of tokens given another observed sequence. We call the type of problems on modelling sequence pairs as sequence to sequence ... More

Iwasawa Theory for Modular Forms at Supersingular PrimesApr 24 2009Jul 21 2010We generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of even and odd Coleman maps for normalised new forms of arbitrary weights and ... More

Efficient Collection of Connected Vehicle Data based on Compressive SensingJun 06 2018Connected vehicles (CVs) can capture and transmit detailed data like vehicle position, speed and so on through vehicle-to-vehicle and vehicle-to-infrastructure communications. The wealth of CV data provides new opportunities to improve the safety, mobility, ... More

A priori estimate for a family of semi-linear elliptic equations with critical nonlinearityOct 28 2008We consider positive solutions of $\Delta u-\mu u+Ku^{\frac{n+2}{n-2}}=0$ on $B_1$ ($n\ge 5$) where $\mu $ and $K>0$ are smooth functions on $B_1$. If $K$ is very sub-harmonic at each critical point of $K$ in $B_{2/3}$ and the maximum of $u$ in $\bar ... More

Modular curves, invariant theory and $E_8$Apr 06 2017Jun 08 2017The $E_8$ root lattice can be constructed from the modular curve $X(13)$ by the invariant theory for the simple group $\text{PSL}(2, 13)$. This gives a different construction of the $E_8$ root lattice. It also gives an explicit construction of the modular ... More

Prescribing curvatures on three dimensional Riemannian manifolds with boundariesOct 28 2008Let $(M,g)$ be a complete three dimensional Riemannian manifold with boundary $\partial M$. Given smooth functions $K(x)>0$ and $c(x)$ defined on $M$ and $\partial M$, respectively, it is natural to ask whether there exist metrics conformal to $g$ so ... More

Network Representation Using Graph Root DistributionsFeb 27 2018Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. At the core of this framework is the parameterization of graph sampling distributions, where existing methods suffer from non-trivial ... More

A Correction Method for the Density of StatesMay 15 2012We present a correction method for the density of states (DOS) obtained from the generalized ensemble simulations. The DOS is proportionally corrected to match the exact values and/or good approximations known for the system. We demonstrate the validity ... More

Inclusive breakup calculations in angular momentum basis: application to $^7$Li+$^{58}$NiDec 05 2017The angular momentum basis method is introduced to solve the inclusive breakup within the model proposed by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)]. This method is based on the geometric transformation between Jacobi coordinates, ... More

Badly approximable points on manifolds and unipotent orbits in homogeneous spacesMar 09 2017May 01 2019In this paper, we study the weighted $n$-dimensional badly approximable points on manifolds. Given a $C^n$ differentiable non-degenerate submanifold $\mathcal{U} \subset \mathbb{R}^n$, we will show that any countable intersection of the sets of the weighted ... More

Divergent trajectories under diagonal geodesic flow and splitting of discrete subgroups of $\mathrm{SO}(n,1) \times \mathrm{SO}(n,1)$Sep 14 2016May 01 2019Let $H = \mathrm{SO}(n,1)$ and $A = \{a(t): t \in \mathbb{R}\}$ be a maximal $\mathbb{R}$-split Cartan subgroup of $H$. Let $\Gamma \subset H \times H$ be a nonuniform lattice in $H \times H$ and $X_{\Gamma} : = H \times H/ \Gamma$. Let $A_2 : = \{ a_2(t):=a(t) ... More

Monotonicity and Kaehler-Ricci flowNov 13 2002We show a connection between the linear trace Li-Yau-Hamilton inequality for the Kaehler-Ricci flow and the monotonicity formula for the positive currents. As an application of the linear trace Li-Yau-Hamilton stated in this paper and the one proved by ... More

Ancient solution to Kahler-Ricci flowFeb 23 2005Mar 14 2005In this paper, we prove that any non-flat ancient solution to K\"ahler-Ricci flow with bounded nonnegative bisectional curvature has asymptotic volume ratio zero. We also prove that any gradient shrinking solitons with positive bisectional curvature must ... More

Iwasawa Theory for the Symmetric Square of a CM Modular Form at Inert PrimesDec 08 2010Aug 16 2011Let f be a CM modular form and p an odd prime which is inert in the CM field. We construct two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as the one constructed by Delbourgo-Dabrowski, whereas ... More

Poincaré series and modular functions for U(n, 1)May 02 2001We construct infinitely many nonholomorphic automorphic forms and modular forms associated to a discrete subgroup of infinite covolume of $U(n, 1)$.

Geometry and arithmetic associated to Appell hypergeometric partial differential equationsSep 25 2003Dec 16 2004In this paper, we study the monodromy of Appell hypergeometric partial differential equations, which lead us to find four derivatives which are associated to the group GL(3). Our four derivatives have the remarkable properties. We find that Appell hypergeometric ... More

Collisionless Magnetic Reconnection via Alfven EigenmodesJul 04 2009We propose an analytic approach to the problem of collisionless magnetic reconnection formulated as a process of Alfven eigenmodes' generation and dissipation. Alfven eigenmodes are confined by the current sheet in the same way that quantum mechanical ... More

The sharp lower bound for the volume of 3-folds of general type with χ(\Co{X})=1Oct 24 2007Let $V$ be a smooth projective 3-fold of general type. Denote by $K^{3}$, a rational number, the self-intersection of the canonical sheaf of any minimal model of $V$. One defines $K^{3}$ as a canonical volume of $V$. The paper is devoted to proving the ... More

Vanishing and injectivity for R-Hodge modules and R-divisorsSep 10 2018We prove the injectivity and vanishing theorem for R-Hodge modules and R-divisors over projective varieties, extending the results for rational Hodge modules and integral divisors in \cite{Wu15}. In particular, the injectivity generalizes the fundamental ... More

Partial Reduction and Delaunay/Deprit VariablesJan 23 2014Jul 12 2014Based on a concept link between the partial reduction procedure of the reduction of the rotational symmetry of the N-body problem with the symplectic cross-section theorem of Guillemin-Sternberg, we present alternative proofs of the symplecticity of Delaunay ... More

Thresholding for Top-k Recommendation with Temporal DynamicsJun 06 2015Nov 09 2015This work focuses on top-k recommendation in domains where underlying data distribution shifts overtime. We propose to learn a time-dependent bias for each item over whatever existing recommendation engine. Such a bias learning process alleviates data ... More

The universal $n$-pointed surface bundle only has $n$ sectionsNov 14 2016Sep 02 2018The classifying space BDiff$(S_{g,n})$ of the orientation-preserving diffeomorphism group of the surface $S_{g,n}$ of genus $g>1$ with $n$ ordered marked points has a universal bundle \[ S_g \to \text{UDiff}(S_{g,n})\xrightarrow{\pi}\text{BDiff}(S_{g,n}). ... More

The universal surface bundle over the Torelli space has no sectionsOct 02 2017Oct 09 2017For $g>3$, we give two proofs of the fact that the \emph{Birman exact sequence} for the Torelli group \[ 1\to \pi_1(S_g)\to {\cal I}_{g,1}\to {\cal I}_g\to 1 \] does not split. This result was claimed by G. Mess in \cite{mess1990unit}, but his proof has ... More

Section problems for configuration spaces of surfacesAug 26 2017May 20 2019In this paper we give a close-to-sharp answer to the basic questions: When is there a continuous way to add a point to a configuration of $n$ ordered points on a surface $S$ of finite type so that all the points are still distinct? When this is possible, ... More

Surjective homomorphisms between surface braid groupsApr 17 2017Apr 26 2019Let $PB_n(S_{g,p})$ be the pure braid group of a genus $g>1$ surface with $p$ punctures. In this paper we prove that any surjective homomorphism $PB_n(S_{g,p})\to PB_m(S_{g,p})$ factors through one of the forgetful homomorphisms. We then compute the automorphism ... More

Abundance of non-uniruled 3-folds with non-trivial Albanese maps in positive characteristicsOct 12 2016In this paper, we prove abundance for non-uniruled 3-folds with non-trivial Albanese maps, over an algebraically closed field of characteristic $p > 5$. As an application we get a characterization of abelian 3-folds.

On the projective normality of cyclic coverings over a rational surfaceDec 20 2016Apr 09 2019Let $S$ be a rational surface with $\dim|-K_S|\ge 1$ and let $\pi: X\rightarrow S$ be a ramified cyclic covering from a nonruled smooth surface $X$. We show that for any integer $k\ge 3$ and ample divisor $A$ on $S$, the adjoint divisor $K_X+k\pi^*A$ ... More